# Floodwater Utilization Based on Reservoir Pre-Release Strategy Considering the Worst-Case Scenario

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Statistical Analysis of Dry Period Durations

- Step 1: Collect actual rainfall data series from recent years;
- Step 2: Count the series of dry period duration ${d}_{i}$, $i=1,2,\cdots ,m$; $m$ is the number of times that a continuous dry period duration has occurred in the actual rainfall data series;
- Step 3: Determine the shortest dry period duration ${d}_{0}$ and calculate the average dry period duration $\overline{d}$.$$\overline{d}=\frac{1}{m}{\displaystyle \sum _{i=1}^{m}{d}_{i}}$$

#### 2.2. Analysis of Flood Forecast Lead Time

- Step 1: For each flood, the natural forecast lead time was determined according to the measured rainfall and flow process of the basin, as shown in Figure 2.
- Step 2: For a series of historical floods in the basin, step 1 was repeated to obtain a set of forecast lead time data. The statistical characteristic parameters of the series of lead time were calculated using Equations (5) and (6).$${E}_{T}=\frac{{\displaystyle \sum _{i=1}^{n}{T}_{i}}}{n}$$$${S}_{T}=\sqrt{\frac{1}{n-1}{\displaystyle \sum _{i=1}^{n}{({T}_{i}-{E}_{T})}^{2}}}$$
- Step 3: The normal distribution $N({E}_{T},{S}_{T}{}^{2})$ was used to fit the probability distribution density of the flood forecast lead time.

#### 2.3. Calculation of Floodwater Volume Over FLWL

#### 2.4. Analysis of the Worst-Case Scenario

#### 2.5. Case Study Area

^{2}, the average annual rainfall in the reservoir area is 1497 mm, the average annual runoff depth is 777 mm, and the annual runoff volume is 1.088 billion m

^{3}, approximately 20% of which occurs in July. Xianghongdian Reservoir suffered 30 large and small floods from 1998 to 2006; the statistics are shown in Table 1.

^{3}. The FLWL of the Xianghongdian Reservoir is 125 m (with a 1227.1 million m

^{3}storage capacity), at 3 m lower than the normal pool level of 128 m (a 1413 million m

^{3}storage capacity), with a total storage capacity difference of 185.9 million m

^{3}. However, since the 1990s, Xianghongdian Reservoir has experienced few floods and many droughts; aside from 1991, 1994, and 2003–2005, where its level was at the FLWL or above, the reservoir level has been under 125 m. In addition, the Xianghongdian Reservoir together with the Foziling Reservoir must provide 440,000 hm

^{2}of irrigation water to fertile fields downstream. Thus, while ensuring the safety of the basin, it is necessary to implement real-time DC-FLWL in the flood season to reasonably adjust its flood storage and conservation storage, increase the refilling rate at the end of the flood season, and make full use of floodwater resources.

^{3}/s, so the floodwater utilization discharge is 200 m

^{3}/s. The level of safe downstream discharge is 2500 m

^{3}/s, and to leave a sufficient safety margin for the downstream area, the discount coefficient was set to 0.5. In this study, the floodwater resource utilization of Xianghongdian Reservoir was analyzed based on the frequent flood process (10-year flood).

## 3. Results

#### 3.1. Dry Period Duration

#### 3.2. Flood Forecast Lead Time

#### 3.3. Increased Water Storage

#### 3.4. Worst-Case Scenario Analysis

## 4. Discussion

#### 4.1. Analysis of Real-Time Increased Water Storage

#### 4.2. Application of Dry Period Duration Infromation in DC-FLWL

#### 4.3. Floodwater Utilization in the Worst-Case Scenario

## 5. Conclusions

- (1)
- The two-period capacity-constrained pre-release method proposed in this study divided the pre-release process into the water use pre-release period and flood control pre-release period. The method has a clear concept, simple principle, and simple calculation procedure. The research example showed that the method is feasible.
- (2)
- According to the historical rainfall data of the Xianghongdian Reservoir basin, the statistical parameters for the dry period duration have obvious negative index distribution characteristics. Compared with the asymptotic regression model, it is safer to use the negative exponential model to describe the distribution law of the dry period duration.
- (3)
- According to the dry period duration and flood forecast lead time, different floodwater resource utilization scenarios were simulated to establish the relationship between the floodwater volume over the FLWL (i.e., increased water storage), dry period duration, and flood forecast lead time, which can provide support for real-world operation decisions of the reservoir. When Xianghongdian Reservoir had a simulated dry period of 5 days and a flood forecast lead time of 6 h, the reservoir’s floodwater volume over the FLWL was $63.4\times {10}^{6}{\mathrm{m}}^{3}$, and the corresponding water level was 126 m, which was 1.0 m higher than the original FLWL.
- (4)
- Through the analysis of reservoir operations under the worst-case scenario, the flood control burden of the reservoir was quantified, which was helpful in proposing solutions and ensuring the flood control safety of the basin. When the dry period duration of Xianghongdian Reservoir was 5 days and the flood forecast lead time was 6 h, considering the worst-case scenario, the water capacity that could not be released in time was deducted from the original total floodwater volume over the FLWL; a $23.0\times {10}^{6}{\mathrm{m}}^{3}$ of safe floodwater volume over the FLWL was still available.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- McFarlane, D.; Stone, R.; Martens, S.; Thomas, J.; Silberstein, R.; Ali, R.; Hodgson, G. Climate change impacts on water yields and demands in south-western Australia. J. Hydrol.
**2012**, 475, 488–498. [Google Scholar] [CrossRef] - Dettinger, M.D.; Ralph, F.M.; Das, T.; Neiman, P.J.; Cayan, D.R. Atmospheric rivers, floods and the water resources of California. Water
**2011**, 3, 445–478. [Google Scholar] [CrossRef] - Zhai, M.; Lin, Q.; Huang, G.; Zhu, L.; An, K.; Li, G.; Huang, Y. Adaptation of cascade hydropower station scheduling on a headwater stream of the Yangtze River under changing climate conditions. Water
**2017**, 9, 293. [Google Scholar] [CrossRef] [Green Version] - Windsor, J.S. Optimization model for the operation of flood control systems. Water Resour. Res.
**1973**, 9, 1219–1226. [Google Scholar] [CrossRef] - Yun, R.; Singh, V.P. Multiple duration limited water level and dynamic limited water level for flood control, with implications on water supply. J. Hydrol.
**2008**, 354, 160–170. [Google Scholar] [CrossRef] - Diao, Y.; Wang, B. Scheme optimum selection for dynamic control of reservoir limited water level. Sci. China Technol. Sci.
**2011**, 54, 2605–2610. [Google Scholar] [CrossRef] - Zhou, Y.; Guo, S.; Chang, F.; Liu, P.; Chen, A.B. Methodology that improves water utilization and hydropower generation without increasing flood risk in mega cascade reservoirs. Energy
**2018**, 143, 785–796. [Google Scholar] [CrossRef] - Chang, J.; Guo, A.; Du, H.; Wang, Y. Floodwater utilization for cascade reservoirs based on dynamic control of seasonal flood control limit levels. Environ. Eeath Sci.
**2017**, 76, 1–12. [Google Scholar] [CrossRef] - Wang, B.; Zhou, H. Theory, Method and Application of Reservoir Dynamic of the Limited Water Level; Press of Hydraul. And Hydropower of China: Beijing, China, 2006; pp. 1–17. (In Chinese) [Google Scholar]
- Wang, G.; Liang, G.; Wang, B.; Bin, H.E. Dynamic operation of reservoir normal elevation based on rainfall forecast and constrained pre-discharge capacity and its application. J. Hydroelec. Eng.
**2010**, 4, 28–31. (In Chinese) [Google Scholar] - Chou, F.N.F.; Wu, C. Expected shortage based pre-release strategy for reservoir flood control. J. Hydrol.
**2013**, 497, 1–14. [Google Scholar] [CrossRef] - Zhao, Q.; Zhong, P.; Liu, G.; Wan, X.; Wang, Y. Research on dynamic control domain of flood control level of Hekoucun Reservoir based on forecasting operation. Water Resour. Power
**2019**, 37, 56–59. (In Chinese) [Google Scholar] - Zhou, Y.; Guo, S.; Liu, P.; Xu, C. Joint operation and dynamic control of flood limiting water levels for mixed cascade reservoir systems. J. Hydrol.
**2014**, 519, 248–257. [Google Scholar] [CrossRef] - Chen, J.; Guo, S.; Li, Y.; Liu, P.; Zhou, Y. Joint operation and dynamic control of flood limiting water levels for cascade reservoirs. Water Resour. Manag.
**2013**, 27, 749–763. [Google Scholar] [CrossRef] - Withanachchi, S.; Ghambashidze, G.; Kunchulia, I.; Urushadze, T.; Ploeger, A. A paradigm shift in water quality governance in a transitional context: A critical study about the empowerment of local governance in Georgia. Water
**2018**, 10, 98. [Google Scholar] [CrossRef] [Green Version] - Liu, Y.; Gupta, H.V. Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework. Water Resour. Res.
**2007**, 43. [Google Scholar] [CrossRef] - Mascaro, G.; Vivoni, E.R.; Deidda, R. Implications of ensemble quantitative precipitation forecast errors on distributed streamflow forecasting. J. Hydrometeorol.
**2010**, 11, 69–86. [Google Scholar] [CrossRef] [Green Version] - Jain, S.K.; Yoganarasimhan, G.N.; Seth, S.M. A risk-based approach for flood control operation of a multipurpose reservoir. J. Am Water Resour.
**1992**, 28, 1037–1043. [Google Scholar] [CrossRef] - Krzysztofowicz, R.; Duckstein, L. Preference criterion for flood control under uncertainty. Water Resour. Res.
**1979**, 15, 513–520. [Google Scholar] [CrossRef] - Xu, B.; Zhong, P.; Huang, Q.; Wang, J.; Yu, Z.; Zhang, J. Optimal hedging rules for water supply reservoir operations under forecast uncertainty and conditional value-at-risk criterion. Water
**2017**, 9, 568. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Wang, G.; Peng, Y.; Zhou, H. Risk analysis of dynamic control of reservoir limited water level by considering flood forecast error. Sci. China Technol. Sci.
**2011**, 54, 1888–1893. [Google Scholar] [CrossRef] - Li, X.; Guo, S.; Liu, P.; Chen, G. Dynamic control of flood limited water level for reservoir operation by considering inflow uncertainty. J. Hydrol.
**2010**, 391, 124–132. [Google Scholar] [CrossRef] - Hui, R.; Lund, J.; Zhao, J.; Zhao, T. Optimal pre-storm flood hedging releases for a single reservoir. Water Resour. Mang.
**2016**, 30, 5113–5129. [Google Scholar] [CrossRef] - Ding, W.; Zhang, C.; Cai, X.; Li, Y.; Zhou, H. Multiobjective hedging rules for flood water conservation. Water Resour. Res.
**2017**, 53, 1963–1981. [Google Scholar] [CrossRef] - Ding, W.; Zhang, C.; Peng, Y.; Zeng, R.; Zhou, H.; Cai, X. An analytical framework for flood water conservation considering forecast uncertainty and acceptable risk. Water Resour. Res.
**2015**, 51, 4702–4726. [Google Scholar] [CrossRef] - Maggioni, V.; Massari, C. On the performance of satellite precipitation products in riverine flood modeling: A review. J. Hydrol.
**2018**, 558, 214–224. [Google Scholar] [CrossRef] - Ren, M.; He, X.; Huang, J.; Li, H. Real-time dynamic control of reservoir waterlevel in flood season and its risk analysis based on short-term rainfall forecast information. J. Hydraul Eng.
**2013**, 43, 66–72. (In Chinese) [Google Scholar] [CrossRef] - Zhong, Y.; Guo, S.; Ba, H.; Xiong, F.; Chang, F.; Lin, K. Evaluation of the BMA probabilistic inflow forecasts using TIGGE numeric precipitation predictions based on artificial neural network. Hydrol. Res.
**2018**, 49, 1417–1433. [Google Scholar] [CrossRef] - Cai, C.; Wang, J.; Li, Z. Assessment and modelling of uncertainty in precipitation forecasts from TIGGE using fuzzy probability and Bayesian theory. J. Hydrol.
**2019**, 577, 123995. [Google Scholar] [CrossRef] - Cai, C.; Wang, J.; Li, Z. Improving TIGGE Precipitation Forecasts Using an SVR ensemble approach in the Huaihe River Basin. Adv. Meteorol.
**2018**, 2018, 1–15. [Google Scholar] [CrossRef] - Lin, H.; Zhong, P.; Liu, G.; Wan, X.; Wang, Y.; Lu, L. A method of determining the timing of water storage during dynamic control of flood limited water level in the reservoir. China Rural Water Hydropower
**2019**, 9, 157–161. (In Chinese) [Google Scholar] - Ding, W.; Zhou, H. Dynamic control of flood limited water level for reservoirs: Developments and trends. China Flood Drought Manag.
**2018**, 28, 6–10. (In Chinese) [Google Scholar] [CrossRef] - Qu, Y.; Sun, G.; Li, Z. The maximum entropy principle and its applications. J. Qingdao Inst. Architect. Eng.
**1996**, 17, 94–100. (In Chinese) [Google Scholar] - Wan, X.; Yang, Q.; Jiang, P.; Zhong, P.A. A hybrid model for real-time probabilistic flood forecasting using Elman Neural Network with heterogeneity of error distributions. Water Resour. Manag.
**2019**, 33, 4027–4050. [Google Scholar] [CrossRef] - Bao, H.J.; Zhao, L.N.; He, Y.; Li, Z.J.; Manful, D. Coupling ensemble weather predictions based on TIGGE database with Grid-Xinanjiang model for flood forecast. Adv. Geosci.
**2011**, 29, 61–67. [Google Scholar] [CrossRef] [Green Version] - Cloke, H.L.; Pappenberger, F. Ensemble flood forecasting: A review. J. Hydrol.
**2009**, 375, 613–626. [Google Scholar] [CrossRef]

**Figure 1.**Two-period capacity-constrained pre-release method. Note: outflow is the drainage process of the reservoir; inflow is the reservoir inflow process; flood tail is the recession flood stage of the last flood; ${t}_{0}$ is the pre-store time; ${t}_{1}$ is the water use pre-release time; ${t}_{2}$ is the flood control pre-release time; $d$ is the continuous dry period duration, $\tau $ is the flood forecast lead time, ${q}_{m}(t)$ is the daily average utilization discharge (mainly for power generation and various types of water supply) in the dry period, and ${q}_{c}$ is the average flood outflow in the flood forecast period.

**Figure 2.**Natural forecast lead time of a flood. Note: $P$ is the precipitation; $T$ is the flood forecast lead time; ${t}_{1}$ is the end time of the main rainfall; and ${t}_{2}$ is the occurrence time of the flood peak flow.

**Figure 4.**Box and whisker plots of dry period in the basin during 1956–2015. The horizontal line in the box represents the median of the distribution (50% of the data are greater than this value), and the upper and lower box limits represent the upper and lower quartiles (25% of data greater/lower than the value), respectively. Maximum and minimum values are indicated by the top and bottom horizontal lines. The outlier points show values of more than two-thirds of the quantile.

**Figure 7.**Statistical chart of floodwater volume over the flood limited water level (FLWL) in different scenarios.

**Figure 8.**Relationships between the release time and flood forecast lead time in different scenarios. Note: the top left of the indicator line shows that floodwater stored over the FLWL cannot be released completely within the lead time.

Flood Event Date (date/month/year) | Peak Discharge (m ^{3}/s) | Flood Volume (10 ^{6} m^{3}) | Flood Period Duration (h) |
---|---|---|---|

01/09/2005 | 5186 | 513.84 | 110 |

08/07/2003 | 5223 | 476.53 | 111 |

13/08/2004 | 2016 | 236.76 | 131 |

27/06/1999 | 4420 | 231.00 | 46 |

04/07/2003 | 2071 | 104.10 | 60 |

22/06/1999 | 1453 | 89.22 | 73 |

23/06/2002 | 1681 | 79.60 | 27 |

30/05/2004 | 1312 | 66.48 | 32 |

29/06/1999 | 739 | 65.51 | 54 |

22/06/2003 | 813 | 62.40 | 34 |

06/08/2002 | 665 | 60.48 | 46 |

09/05/1998 | 428 | 55.27 | 67 |

26/06/2003 | 842 | 54.50 | 46 |

24/08/1999 | 318 | 51.92 | 79 |

03/08/2005 | 567 | 50.79 | 35 |

22/05/1998 | 483 | 44.75 | 74 |

20/06/2002 | 588 | 42.45 | 45 |

26/07/2006 | 749 | 41.29 | 47 |

05/05/2002 | 847 | 38.12 | 33 |

27/06/2002 | 452 | 36.25 | 36 |

22/07/2006 | 454 | 34.00 | 43 |

10/07/2005 | 439 | 33.24 | 43 |

09/08/2001 | 454 | 30.42 | 72 |

06/05/2003 | 541 | 28.72 | 24 |

18/06/2001 | 427 | 27.50 | 40 |

14/06/2004 | 398 | 26.05 | 52 |

17/08/1998 | 335 | 23.41 | 46 |

18/06/2004 | 400 | 18.51 | 24 |

05/07/2006 | 610 | 17.56 | 21 |

22/08/1999 | 173 | 17.06 | 46 |

Dry Days (d) | P (%) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

0.1 | 1 | 10 | 20 | 30 | 35 | 40 | 45 | 50 | 75 | 95 | |

NED | 36 | 24 | 13 | 9.2 | 7.1 | 6.3 | 5.6 | 5.0 | 4.5 | 2.5 | 1.3 |

ARM | 726 | 647 | 22.8 | 12.4 | 9.0 | 7.8 | 6.9 | 6.1 | 5.3 | 2.8 | 1.3 |

Flood | Lead Time/h | Flood | Lead Time/h |
---|---|---|---|

21/06/2008 | 6 | 08/08/2012 | 9 |

26/06/2009 | 3 | 05/07/2013 | 12 |

10/07/2010 | 12 | 04/07/2014 | 18 |

17/06/2011 | 9 | 09/08/2015 | 18 |

24/06/2011 | 9 | 30/06/2016 | 3 |

Increased Water Storage (10^{6} m^{3}) | Dry Days (d) | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | ||

Lead time (h) | 1 | 14.28 | 23.47 | 31.44 | 38.29 | 44.01 |

2 | 18.25 | 27.46 | 35.46 | 42.32 | 48.06 | |

3 | 22.17 | 31.41 | 39.43 | 46.32 | 52.07 | |

4 | 26.06 | 35.33 | 43.37 | 50.28 | 56.05 | |

5 | 29.79 | 39.08 | 47.15 | 54.08 | 59.86 | |

6 | 33.24 | 42.56 | 50.65 | 57.60 | 63.40 | |

7 | 36.26 | 45.61 | 53.72 | 60.69 | 66.51 | |

8 | 38.69 | 48.07 | 56.21 | 63.20 | 69.03 | |

9 | 40.84 | 50.25 | 58.41 | 65.42 | 71.27 | |

10 | 43.02 | 52.46 | 60.64 | 67.67 | 73.54 |

Release Time (h) | Dry Days (d) | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | ||

Leading time (h) | 1 | 3.58 | 5.86 | 7.83 | 9.51 | 10.90 |

2 | 4.59 | 6.89 | 8.87 | 10.56 | 11.96 | |

3 | 5.61 | 7.92 | 9.91 | 11.61 | 13.02 | |

4 | 6.62 | 8.95 | 10.95 | 12.66 | 14.09 | |

5 | 7.69 | 10.05 | 12.09 | 13.83 | 15.27 | |

6 | 8.76 | 11.18 | 13.26 | 15.04 | 16.52 | |

7 | 9.91 | 12.42 | 14.59 | 16.43 | 17.97 | |

8 | 11.10 | 13.73 | 16.01 | 17.94 | 19.55 | |

9 | 12.19 | 14.93 | 17.30 | 19.31 | 20.99 | |

10 | 13.27 | 16.10 | 18.55 | 20.63 | 22.37 |

Safe Increased Water Storage Level (10^{6} m^{3}) | Dry Days (d) | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | ||

Lead time (h) | 1 | 3.99 | 4.01 | 4.02 | 4.03 | 4.04 |

2 | 7.95 | 7.97 | 8.00 | 8.02 | 8.03 | |

3 | 11.86 | 11.90 | 11.94 | 11.97 | 11.99 | |

4 | 15.74 | 15.79 | 15.84 | 15.88 | 15.92 | |

5 | 19.38 | 19.45 | 19.51 | 19.56 | 19.60 | |

6 | 22.76 | 22.84 | 22.91 | 22.98 | 23.03 | |

7 | 25.60 | 25.70 | 25.78 | 25.86 | 25.92 | |

8 | 27.89 | 28.00 | 28.09 | 28.18 | 28.25 | |

9 | 30.16 | 30.28 | 30.39 | 30.49 | 30.56 | |

10 | 32.43 | 32.57 | 32.69 | 32.79 | 32.88 |

Flood Event Date (date/month/year) | Start Time | Start Water Level (m) | Storage at the Start Time (10^{6} m^{3}) | Real-time Increase in Water Storage (10^{6} m^{3}) |
---|---|---|---|---|

27/06/1999 | 20:00 | 110.07 | 526.1 | 208.7 |

06/05/2003 | 14:00 | 126.76 | 1335 | 10.1 |

08/07/2003 | 5:00 | 123.1 | 1117.6 | 396.7 |

30/05/2004 | 20:00 | 122.37 | 1077.1 | 37.7 |

03/08/2005 | 20:00 | 120.32 | 968.6 | −25.2 |

26/07/2006 | 5:00 | 121.41 | 1025.7 | −23.5 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hua, L.; Wan, X.; Wang, X.; Zhao, F.; Zhong, P.; Liu, M.; Yang, Q.
Floodwater Utilization Based on Reservoir Pre-Release Strategy Considering the Worst-Case Scenario. *Water* **2020**, *12*, 892.
https://doi.org/10.3390/w12030892

**AMA Style**

Hua L, Wan X, Wang X, Zhao F, Zhong P, Liu M, Yang Q.
Floodwater Utilization Based on Reservoir Pre-Release Strategy Considering the Worst-Case Scenario. *Water*. 2020; 12(3):892.
https://doi.org/10.3390/w12030892

**Chicago/Turabian Style**

Hua, Lijuan, Xinyu Wan, Xianhui Wang, Fangzheng Zhao, Ping’an Zhong, Moyang Liu, and Qingyan Yang.
2020. "Floodwater Utilization Based on Reservoir Pre-Release Strategy Considering the Worst-Case Scenario" *Water* 12, no. 3: 892.
https://doi.org/10.3390/w12030892